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Expected Value Problem Help

  • Thread starter Forumite
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  • #1
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1. A city has 74,806 registered automobiles. Each is required to display a bumper decal showing that the owner paid an annual wheel tax of $50. By law, new decals needed to be purchased during the month of the owner’s birthday. How much wheel tax revenue can the city expect to receive in November?



2. expected value = E(X) = summation(x*f(x))
Leibnitz's rule




3. I thought there was not enough information in the problem. Can we assume that people are equally likely to be born in the different months of the year?
Anyway, all I have is E(X) = (74,506*50)*1/12
where the part in parenthesis is x and 1/12 is the probability function
(not sure).
 

Answers and Replies

  • #2
Ibix
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I think you are right that you need to assume a uniform distribution of birthdays, and I would write that assumption out explicitly.

Just one question about your answer - what is the expected revenue in (say) February?
 
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Going by the same approach, it would be the same answer. Did you have something else in mind?
 
  • #4
Ibix
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I think each day is equally likely...
 
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Ah, I see. So for November, E(X) = (74,506*50)*30/365
and for February, assuming it's not a leap year, it would be E(X) = (74,506*50)*28/365

Thanks for the help.
 
  • #6
Ibix
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That is the right answer for a non-leap year - can you figure it out for an average year?
 

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